Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
(x−2)∣x−2∣1
Evaluate
∣x−2∣1×x−21
Multiply the terms
∣x−2∣×(x−2)1
Solution
(x−2)∣x−2∣1
Show Solution
Find the excluded values
x=2
Evaluate
∣x−2∣1×x−21
To find the excluded values,set the denominators equal to 0
∣x−2∣=0x−2=0
Solve the equations
More Steps
Evaluate
∣x−2∣=0
Rewrite the expression
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x−2=0
Solve the equations
More Steps
Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x=2
Solution
x=2
Show Solution
Find the roots
x∈∅
Evaluate
∣x−2∣1×x−21
To find the roots of the expression,set the expression equal to 0
∣x−2∣1×x−21=0
Find the domain
More Steps
Evaluate
{∣x−2∣=0x−2=0
Calculate
More Steps
Evaluate
∣x−2∣=0
Rewrite the expression
x−2=0
Move the constant to the right side
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
{x=2x−2=0
Calculate
More Steps
Evaluate
x−2=0
Move the constant to the right side
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
{x=2x=2
Find the intersection
x=2
∣x−2∣1×x−21=0,x=2
Calculate
∣x−2∣1×x−21=0
Multiply the terms
More Steps
Multiply the terms
∣x−2∣1×x−21
Multiply the terms
∣x−2∣×(x−2)1
Multiply the terms
(x−2)∣x−2∣1
(x−2)∣x−2∣1=0
Cross multiply
1=(x−2)∣x−2∣×0
Simplify the equation
1=0
Solution
x∈∅
Show Solution